Born in Marksville, the seat of Avoyelles Parish, Overton was the youngest son of Judge Thomas Overton and the former Laura Waddill. He graduated from Louisiana State University in Baton Rouge in 1895, from Tulane University in New Orleans in 1897, and was admitted to the Louisiana bar in 1898.
He established a law practice with four partners in Alexandria and was the city attorney as well. He was a member of the LSU Board of Supervisors. In 1905, he married the former Ada Ruth Dismukes of Natchitoches, and they had three daughters, Katharine (born 1910), Ruth (born 1912) and Mary Elizabeth (born 1916), and a son, John H. Overton, Jr., (1914-1946).
In 1918, Overton ran for the U.S. Senate but was defeated by Edward J. Gay of Plaquemine in Iberville Parish. Overton became a staunch supporter of Huey Pierce Long, Jr., and served as Long's counsel in the latter's impeachment proceedings in 1929.
He was elected to Congress to fill the Eighth District U.S. House seat vacated by the death of Representative James B. Aswell of Natchitoches. He served in the House for slightly less than one term: from May 12, 1931, to March 3, 1933.
In 1932, he ran successfully for the U.S. Senate. He defeated the incumbent Edwin S. Broussard of New Iberia for the Democratic senatorial nomination, then equivalent to election in Louisiana. Broussard charged fraud and voter irregularities. A Senate investigating committee held months of hearings beginning in February 1933. Overton was nevertheless seated without opposition on the then first day of the congressional session, March 4.
Overton was reelected in 1938 and 1944, as has been traditional with incumbent Democratic senators in Louisiana. His committee memberships included Appropriations, Manufactures, Commerce, and Irrigation and Reclamation. His chief area of interest was in flood control and river and harbor development.
He was a segregationist; he opposed an amendment to the Selective Service Act of 1940 that allowed the voluntary enlistment of minorities, on the grounds that it could lead to mixed units. He was quoted in 1947 as having said that "the Democratic South stands for white supremacy".
Overton attempted to withdraw from reelection race in 1944. However, his Louisiana colleague, Allen J. Ellender, circulated a letter urging him to run. The letter was signed by all Democrats then in the Senate.
Overton's last term was cut short by his death at Bethesda Naval Hospital in Bethesda, Maryland. His remains were buried at Mount Olivet Cemetery in Pineville in Rapides Parish. His house in Alexandria was added to the National Register of Historic Places in 1985. In 1998, Overton was posthumously inducted into the Louisiana Political Museum and Hall of Fame in Winnfield.